Fluid dispensers are known utilizing piston pumps to dispense fluids with movement of a piston through a full piston stroke. The present inventors have appreciated that such known dispensers suffer disadvantages when the piston is moved through a lesser stroke than the full piston stroke, particularly when the lesser stroke commences at the same extended position but travels inwardly a lesser extent than in a full piston stroke. These disadvantages include difficulties in dispensing fluid proportionate to the stroke length and difficulties in initial priming of the pump so as to replace air in the pump chamber with liquid.